Advances made by Ralph Greenberg, Jan Nekovar, Cornut and Vatsal, Bertolini and Darmon, Kazuyo Kato, and others, have given us the tools to understand the Selmer module of an elliptic curve over Q relative to Z_p-power extensions of (abelian) number fields, for p a good, ordinary prime for E. Karl Rubin and I have been using these tools to construct, and examine, certain skew-Hermitian matrices over the p-adic group rings of the Galois groups of Z_p-power extensions that contain this arithmetic information. The point of my lecture is to briefly describe this project, recent related results, and open questions.